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Achievable Outcomes in Smooth Dynamic Contribution Games

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  • Steven A. Matthews

    () (Department of Economics, University of Pennsylvania)

Abstract

This paper studies a class of dynamic voluntary contribution games in a setting with discounting and neoclassical payoffs (differentiable, strictly concave in the public good, and quasilinear in the private good). An achievable profile is the limit point of a subgame perfect equilibrium path -- the ultimate cumulative contribution vector of the players. A profile is shown to be achievable only if it is in the undercore of the underlying coalitional game, i.e., the profile cannot be blocked by a coalition using a component-wise smaller profile. Conversely, if free-riding incentives are strong enough that contributing zero is a dominant strategy in the stage games, then any undercore profile is the limit of achievable profiles as the period length shrinks. Thus, in this case when the period length is very short, (i) the set of achievable contributions does not depend on whether the players can move simultaneously or only in a round-robin fashion; (ii) an efficient profile can be approximately achieved if and only if it is in the core of the underlying coalitional game; and (iii) any achievable profile can be achieved almost instantly.

Suggested Citation

  • Steven A. Matthews, 2008. "Achievable Outcomes in Smooth Dynamic Contribution Games," PIER Working Paper Archive 08-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:08-028
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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/08-028.pdf
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    References listed on IDEAS

    as
    1. Leslie M. Marx & Steven A. Matthews, 2000. "Dynamic Voluntary Contribution to a Public Project," Review of Economic Studies, Oxford University Press, vol. 67(2), pages 327-358.
    2. Duffy, John & Ochs, Jack & Vesterlund, Lise, 2007. "Giving little by little: Dynamic voluntary contribution games," Journal of Public Economics, Elsevier, vol. 91(9), pages 1708-1730, September.
    3. Ben Lockwood & Jonathan P. Thomas, 2002. "Gradualism and Irreversibility," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 339-356.
    4. Pitchford, Rohan & Snyder, Christopher M., 2004. "A solution to the hold-up problem involving gradual investment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 88-103, January.
    5. Compte, Olivier & Jehiel, Philippe, 2003. "Voluntary contributions to a joint project with asymmetric agents," Journal of Economic Theory, Elsevier, vol. 112(2), pages 334-342, October.
    6. Ochs, Jack & Park, In-Uck, 2010. "Overcoming the coordination problem: Dynamic formation of networks," Journal of Economic Theory, Elsevier, vol. 145(2), pages 689-720, March.
    7. Huseyin Yildirim, 2006. "Getting the Ball Rolling: Voluntary Contributions to a Large-Scale Public Project," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(4), pages 503-528, October.
    8. Choi, Syngjoo & Gale, Douglas & Kariv, Shachar, 2008. "Sequential equilibrium in monotone games: A theory-based analysis of experimental data," Journal of Economic Theory, Elsevier, vol. 143(1), pages 302-330, November.
    9. Olivier Compte & Philippe Jehiel, 2004. "Gradualism in Bargaining and Contribution Games," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 975-1000.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    dynamic games; monotone games; core; public goods; voluntary contribution; gradualism;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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